Learn English – bother someone “for” something

We should distinguish between different lexical meanings of each word, since each meaning will have different grammatical and semantic requirements. Based on my own understanding, for the basic meaning of "speak" and "talk", "speak" refers to the actual act of saying something, and corresponds to the intransitive version of "say", whereas "talk" refers to the act of engaging in communication with others. This difference explains many of your examples, but not all, since some appear to arise due to different lexical meanings.

Examples of the distinction between basic "speak" and "talk"

• "speak up", "speak out", "speak clearly", "speak confidently/authoritatively": These show that "speak" has to do with the act of saying something.

• "actions speak louder than words", "speaks to the heart", "the clock spoke": Similarly these refer to things figuratively saying something. "talk" would be inappropriate here because these things are not having any conversation.

• "speak for everyone": This refers to being a representative voice, so "talk" doesn't work.

• "grammatically speaking", "so to speak", "speaking of", "talking about": "speak" refers to the actual verbalization, hence "speaking of X", while "talk" refers to the communication, hence "talking about X".

• "talkative": It means "like to talk" or "talks a lot", which is about communicating with others.

• "speak to", "talk to": Usually there is hardly a difference, but the distinction becomes clearer in certain situations. Anyone can "speak to the king" if given the opportunity, but to "talk to the king" suggests further that it is a conversation and not just one-way. In contrast, "speak with" conveys the sense of both speaking to one another, so I doubt it is distinguished from "talk with" in actual usage.

• "spoke about X", "talked about X": "spoke about X" conveys just the speaking, while "talked about X" conveys speaking to others. But for this example both convey the same thing when taken in context.

A few examples of other lexical meanings

• "spoke wise words", "speak English", "speak the truth": It is a different meaning of "speak" that is transitive. Nevertheless, there seems to be still a relation to the above distinction. We can say "talked to them in words of wisdom" and "talk to them in English".

• "I'm talking grammar here": A transitive meaning of "talk". This can be used in place of "grammatically speaking", but conveys talking to the audience about grammar rather than simply stating something.

• "give a talk", "give a speech": The noun "talk" just happens to be spelt the same as the verb.

By the way, I just found out that http://www.thefreedictionary.com/speak mentions roughly the same distinction as I did, but I disagree with what it says about telephone calls. I don't think there is anything wrong with asking to talk to someone on the phone. I don't even think it is less formal today.

Yes, it is a quite a common verb used referring to circumstances or situations:

To arise:(int.)

• to come into being; originate
• to appear; spring up: New problems arise daily.

Ngram: circumstances arise/arose vs situations arise/arose

• ‘If circumstances arise, and you might be forced to leave, then who knows’ – Sean O’Brien.

(www.the42.ie/6-nations-ireland-wales-sean-obrien)

• However, thanks chiefly to the changes brought about in the world sugar market by the Cuban Revolution, circumstances arose that altered the course of events.

(Diagnosis of the Brazilian Crisis)